Entrainment coefficient and effective mass for conduction neutrons in neutron star crust: simple microscopic models

In the inner crust of a neutron star, at densities above the "drip" threshold, unbound "conduction" neutrons can move freely past through the ionic lattice formed by the nuclei. The relative current density nⁱ=nv^¯i of such conduction neutrons will be related to the corresponding mean particle momentum p_i by a proportionality relation of the form nⁱ=Kpⁱ in terms of a physically well defined mobility coefficient K whose value in this context has not been calculated before. Using methods from ordinary solid state and nuclear physics, a simple quantum mechanical treatment based on the independent particle approximation, is used here to formulate K as the phase space integral of the relevant group velocity over the neutron Fermi surface. The result can be described as an "entrainment" that changes the ordinary neutron mass m to a macroscopic effective mass per neutron that will be given—subject to adoption of a convention specifying the precise number density n of the neutrons that are considered to be "free"—by m_⋆=n/K. The numerical evaluation of the mobility coefficient is carried out for nuclear configurations of the "lasagna" and "spaghetti" type that may be relevant at the base of the crust. Extrapolation to the middle layers of the inner crust leads to the unexpected prediction that m_⋆ will become very large compared with m.